Coalescence temperature method

Since the rate of coalescence depends on the frequency difference between the exchanging sites, it will be different for each nucleus and site and will also depend on the magnetic field at which the experiment is carried out. This fact can be exploited to determine the temperature dependency of the rate constants using the coalescence temperature method. 

When the data in this table are plotted, the graph shown in Fig. 33 is obtained. From this one can calculate a pKa of 2.85 for displacement of benzimidazole in D2O. In addition, since room temperature is above the coalescence temperature, it is possible to set a lower limit on the exchange rate between coordinated and uncoordinated benzimidazole of 3.1 X 102 sec-1. From Fig. 33 one can, by extrapolation, calculate the C(20)-methyl resonance of the base-on and "base-off forms to be 0.41 and 1.05 respectively. These numbers can be used, with the assumption of fast exchange, to determine the relative amounts of "base-on and base-off" species from the observed C(20)-chemical shift for any arbitrary sample. Such information would be useful, for instance, when investigating the displacement of benzimidazole by other Lewis bases. Thus for the simple case of benzimidazole displacement we have shown that NMR provides a method for studying the molecular conformation of vitamin B12. 

Rate process with activation energies between 6 and 25 kcal mol-1 can be studied conveniently by the NMR method. Line shape theories have been well reviewed.103 In most cases a single rate constant k is estimated at the coalescence temperature, and AG is obtained from the Eyring equation. For exchange between two unequally populated sites, AG for the forward and reverse reactions are different. This is an important point to be considered in the case of nitrogen inversion phenomena. 

There has been a controversy 54 89) regarding the accuracy of equations (iii) and (iv), i.e. the validity of inferring rate constants from coalescence temperatures. It now appears B9) that, provided no additional coupling is present, and provided Av > 3 Hz (eqn. (iii)) and Av > J (eqn. (iv)), the simple coalescence method gives rate constants within 25 % of those obtained by more sophisticated line shape analysis (vide infra). This leads to an error in AG° no greater than that produced by the uncertainty of temperature measurement ( 2 °C m) in the NMR probe. 

Activation parameters at coalescence temperature show that the coordinate interaction in these compounds is not a function of the electronegativity of X but is controlled by the ability of the nitrogen atom to stretch the Si—X bond. The tendency of the silicon atom to increase its valency decreases in the order X = OCOR, Br, Cl > SR F > OR, H This sequence corresponds directly to the rate of racemization of halosilanes and to the substitution of R3SiX with inversion of configuration Although no intramolecular coordination was observed in solutions of acetoxysilanes (CH3) Si(OCOR)4 by the Si NMR method the shape of the H NMR spectra of these compounds with chiral silicon atom points to Si -0 interaction... 

For those planning the use DNMR to evaluate barriers, the evaluations of sources of error covered in Section 1.1 and other published articles should be consulted. A caveat to consider the definition of rate constant carefully is in order. The author recommends the use of equation (3) and substitution into the Eyring equation as the most rehable method for obtaining an experimental value for AG. Owing to the large errors, which can arise, the use of coalescence temperatures and rate expressions at should be avoided at all costs. As primitive as it may seem, reference to Table 1 can provide a fairly accurate value for AG in most cases. 

A second method, first introduced by Gutowsky and Holm (1956), is to measure the change in apparent chemical shift in the region where the two peaks collapse to one. In the case where A and B are equally populated ta = rB = 2r andpA = pB. Equation (27) for the r-mode gives two minima of signal at — a and + a, two maxima for the absorption peaks and a minimum between these. Above the coalescence temperature the two maxima coincide. Differentiation of equation (27) with respect to Aoi allows a location of these maxima (Gutowsky and Holm, 1956). The result is... 

The effect of amide structure on the rotation barrier was the object of more precise work in the study of Rogers and Woodbury (1962). Several methods for analysing the rate processes from steady-state spectra were combined. The energy barriers and frequency factors are summarized in Table 5. There is some variation in the coalescence temperature Tc and the energy barriers Ea. Agreement with Gutowsky and Holm (1956) for the molecule AW-dimethylacetamide is good, but... 

NMR spectral techniques are widely used to study complexation of macrocycles as well as the thermodynamic and kinetic quantities that describe host-guest interactions. Measurements of the free energy of activation for complex dissociation (AG. ) at the H NMR coalescence temperature, have been done using a variable temperature H NMR procedure . The method is advantageous for ammonium cations because the dissociation rate for most crown ether-ammonium cation complexes is within the H NMR time scale and only a small amount of sample (3-5 mg) is required. 

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